# Symmetry Group P2

There are only 17 methods to divide the two dimensional surface into true tessellations. These 17 rules were derived from the observation and study of crystallography, a long time ago.  They are the basis for many other disciplines as well, wallpaper designs, fabric design, wrapping paper, ceramic tiles… But my passion lies with classic tessellations, where the same odd shapes repeat to fill a surface with an absolutely tight perfect fit. Well, I try, anyhow.

The Tofino Hitchhiker was built using this P2 symmetry system.

Symmetry Group P2 – Tofino Hitchhiker – © 2013 Champagne Design

### Symmetry Group P2

I’ve come to call this symmetry group the “triple whip”. The system is based on a four sided grid, which can be skewed into lozenges, parallelograms. Each of the corners has a two-fold rotation point. One of them, slightly special. If three lines are drawn from that corner, each to one other corner, a perfectly repeating shape is formed. I look at these, I’ve drawn them, but can never quite put it into words as well. The triple whip drawing below, explains it better. Note, rotation point R2, has the 3 whips extending to the other 3 corners. No mirrors or glides here, so your lines can wander over the parallelogram’s delineation.

Symmetry Group P2, explained

The Hiker image below, when zoomed-out, plainly shows the parallelogram, helped by the horizontal belt and hiking pole of course. Rotation points occur at his right hand, left SO4 watch, top of one boot and bottom of the other. See the 6 red dots. Two of the parallelograms are required to translate the full figure. I’ve read another explanation, where a parallelogram has 4 two-fold rotation points, midway on each side and a fifth two-fold rotation in the middle. But that just confuses me.

Symmetry Group P2 – © 2013 Champagne Design, Vancouver Island Hiker

Twelve symmetry groups explained and illustrated to date. I have a bit more work to do, 5 more groups. Till then,

Lots of software out there to help you accomplish this type of design.

1. An iPad app is available, which is what I have used here to create these images: KaleidoPaint by Jeff Weeks.
2. There is also a java-based program “Escher Web Sketch”  at the Ecole Polytechnique de Lausanne. Make sure Java is enabled and not blocked by your security software.
3. Also, another screen-based software by Anselm Levskaya Escher Sketch v2.
4. Or a pair of scissors and a piece of cardboard works quite well. That’s how I learned.

If you’re a “Learn by Seeing” “Learn by Doing” kind of person, I’ve started creating videos on “how-to” create tessellations. I’ll be covering each of the 17 symmetry groups, one class at a time. And like all artists, we need to make a living. So. I’ve uploaded these to the Skillshare platform. I’ll get paid by minutes watched.

You can register for just a month and cancel anytime. It’s less than the cost of a Netflix subscription! And you can still stay put on the couch. There are over 40,000 classes on topics for creative persons just like you. Join my mailing list, either here on my blog (in the sidebar), or a at this link for a specific list I use to announce new classes.

I’d love for you to join me on this wonderful learning adventure.

If you prefer, you can follow my progress on social media, I always announce my new class:
Facebook: Franc Champagne, and Vancouver Island Tessellation Artist
Instagram: champagne.francine
Linkedin: Graphic Design, PowerPoint and tessellations
Youtube: Video animations and class intros

My classes have received an independent rating of 9.7/10, placing these Skillshare classes in the TOP 2% of classes reviewed by CourseMarks!

🙂

Here is a list of the classes up so far:

1. Rekindle your Love of M.C. Escher Tessellations, draw your own tessellations using a free iPad App. In this class I introduce the concept of tessellations, show you the work of M.C. Escher as well as other artists. Then we dive into a first symmetry method, P4g, accomplished by drawing only one line to create the perimeter of your tessellation.
2. Just like M. C. Escher’s Tessellations: Draw Using a New Symmetry Method and Your iPad. We tackle the Mirrored Triplets symmetry group, aka P3m1.
3. This UP/DOWN, LEFT/RIGHT Tessellation method was M. C. Escher’s favorite. It is also the symmetry method, P1, most taught in schools. Probably the only way most artists have tried to accomplish a nested shape. We will push it a tad farther, but also easier than scissors and cardboard.
4. M. C. Escher Tessellations: The Three Cozy Buddies Symmetry Group, know as symmetry group P3. Lots of examples, from many different tessellation artists. One of my favorite ways of creating tessellations.
5. Digital Patterns: Super Simple Quickie Patterns. 20 patterns in 30 minutes! I will show you how to draw and assemble your pattern design elements in four different and unusual ways. Come explore the possibilities, from a different point of view using your iPad and the free KaleidoPaint app. There is more to symmetry than rigid repeats, half-drops and tossed layouts.
6. My next class with deal with a symmetry group I have named: “This way — that way”, aka crystallographic notation Pg. That Koloman Moser video above, is part of the series.

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